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Heat Transfer: Coffee in a Thermos

Who loves coffee? That’s what I thought; most of you. I for one cannot go a day without fueling up on coffee. Now that fall is on its way, the cooler weather will require better insulation of my coffee when I take it to-go, in the name of a travel mug (i.e., a thermos). This leads me to wonder: how long will coffee stay warm inside a thermos if I bring it outside?

Luckily, my colleague John Dunec has already worked out the answer to this caffeine-inspired thermos problem. Turns out, the cooling of a liquid inside a thermos can be solved using multiphysics simulations. There are two ways you can look at this problem:

As a convection coefficient (h) problem

As a heat transfer coupled with CFD problem

In a recent heat transfer webinar John showed both examples, and at first it seemed as though each option provided the same answer. Usually one starts with a constant h, but then he said that because the temperature keeps changing you keep ending up with a different h for each time spent of your simulation. So the first approach might not be the most accurate — even though it’s the quickest and can give you useful insight about your application — after all. (By the time you’re through solving for h over and over your coffee will be cold!) Have a look at the equation for h:

Here, NuL is a rather complex experimental correlation dependent on RaL, which of course is dependent on the temperature. A change in temperature would therefore prompt multiple computations in order to solve for the convection coefficient h. This approach allows us to model the heat transfer and CFD occurring in the surrounding air; all the physics involved are represented by an experimental correlation. COMSOL Multiphysics can help you with the first approach if you’re looking for a quick solution: you can simply input your correlations or choose them from the library.

On the other hand, you could choose the second approach and solve this as a heat transfer and CFD problem using COMSOL Multiphysics. In that case, you don’t have to enter or select experimental correlations on your own, COMSOL will solve for the heat transfer in the thermos and for the heat transfer and CFD in the surrounding air and couple these physics together. This time there are no approximations coming into play: your geometry and real boundary conditions will be taken into account.

So actually, not only can this be solved using multiphysics — it should be solved that way. Now enjoy your hot cup of coffee.